The grades on a physics midterm at Santa Rita are normally distributed with $\mu = 80$ and $\sigma = 3.5$. William earned a n $84$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{84 - {80}}{{3.5}}} $ ${ z \approx 1.14}$ The z-score is $1.14$. In other words, William's score was $1.14$ standard deviations above the mean.